Nothing
is.positive.definite <- function( x, tol=1e-8 )
{
###
### this function determines if the given real symmetric matrix is positive definite
###
### parameters
### x = a square numeric matrix object
### tol = tolerance level for zero
###
if ( !is.square.matrix( x ) )
stop( "argument x is not a square matrix" )
if ( !is.symmetric.matrix( x ) )
stop( "argument x is not a symmetric matrix" )
if ( !is.numeric( x ) )
stop( "argument x is not a numeric matrix" )
eigenvalues <- eigen(x, only.values = TRUE)$values
n <- nrow( x )
for ( i in 1: n ) {
if ( abs( eigenvalues[i] ) < tol ) {
eigenvalues[i] <- 0
}
}
if ( any( eigenvalues <= 0 ) ) {
return( FALSE )
}
return( TRUE )
}
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